I started looking into possible internal leaks and failed seals when Jeff the moto-Jedi, who now lives four thousand kilometres away on Canada's beautiful west coast, suggested detaching the caliper and hanging it down low so air has another way to escape. With the caliper hanging upside down and low down, I re-bled the system and it immediately firmed up.
If you're having trouble getting air out of your brake lines, change the geometry of what you're working on and bleed again. I figured my good hand pump and would pull fluid through the system well enough to move any bubbles, but there is no substitute for geometry... or gravity.
Top Tip: if you're having trouble bleeding a system, take the calipers off and try them in a different position. The Tiger's rear brake is as tight as a drum now.